Abstract:
Muon Colliders have unique technical and physics advantages and disadvantages when compared with both hadron and electron machines. They should thus be regarded as complementary. Parameters are given of 4 TeV and 0.5 TeV high luminosity \mumu colliders, and of a 0.5 TeV lower luminosity demonstration machine. We discuss the various systems in such muon colliders, starting from the proton accelerator needed to generate the muons and proceeding through muon cooling, acceleration and storage in a collider ring. Problems of detector background are also discussed.

Abstract:
We point out that both the specific lepton number content and the high energies potentially attainable with muon-muon colliders make it advisable to consider the technical feasibility of including an option of like-sign incoming beams in the studies towards a proposal to build a muon-muon collider with center-of-mass energies in the TeV region. This capability will add some unique physics capabilities to the project. Special attention will have to be paid to polarization retention for the muons.

Abstract:
Novel magnetic helical channel designs for capture and cooling of bright muon beams are being developed using numerical simulations based on new inventions such as helical solenoid (HS) magnets and hydrogen-pressurized RF (HPRF) cavities. We are close to the factor of a million six-dimensional phase space (6D) reduction needed for muon colliders. Recent experimental and simulation results are presented.

Abstract:
Conceptual design studies are underway for muon colliders and other high-current muon storage rings that have the potential to become the first true ``neutrino factories''. Muon decays in long straight sections of the storage rings would produce precisely characterized beams of electron and muon type neutrinos of unprecedented intensity. This article reviews the prospects for these facilities to greatly extend our capabilities for neutrino experiments, largely emphasizing the physics of neutrino interactions.

Abstract:
Neutrino radiation is expected to impose major design and siting constraints on many-TeV muon colliders. Previous predictions for radiation doses at TeV energy scales are briefly reviewed and then modified for extension to the many-TeV energy regime. The energy-cubed dependence of lower energy colliders is found to soften to an increase of slightly less than quadratic when averaged over the plane of the collider ring and slightly less than linear for the radiation hot spots downstream from straight sections in the collider ring. Despite this, the numerical values are judged to be sufficiently high that any many-TeV muon colliders will likely be constructed on large isolated sites specifically chosen to minimize or eliminate human exposure to the neutrino radiation. It is pointed out that such sites would be of an appropriate size scale to also house future proton-proton and electron-positron colliders at the high energy frontier, which naturally leads to conjecture on the possibilities for a new world laboratory for high energy physics. Radiation dose predictions are also presented for the speculative possibility of linear muon colliders. These have greatly reduced radiation constraints relative to circular muon colliders because radiation is only emitted in two pencil beams directed along the axes of the opposing linacs.

Abstract:
The potential of muon colliders to address fundamental physics issues is explored, with emphasis on understanding the nature of electroweak symmetry breaking. The $s$-channel production of Higgs bosons, unique to a muon collider, along with precision measurements of W^+W^-, t\bar t, and Zh thresholds would determine the properties of Higgs bosons and test electroweak radiative corrections. At the high energy frontier, a 4 TeV muon collider is ideally suited to study either the production of supersymmetric scalar particles or a strongly interacting WW sector.

Abstract:
Over the last decade there has been significant progress in developing the concepts and technologies needed to produce, capture and accelerate O(1021) muons/year. This development prepares the way for a new type of neutrino source (Neutrino Factory) and a new type of very high energy lepton-antilepton collider (Muon Collider). This article reviews the motivation, design and R&D for Neutrino Factories and Muon Colliders.

Abstract:
A number of recent developments have led to simulations of an inverse cyclotron for cooling intense muon beams for neutrino factories and muon colliders. Such a device could potentially act as a novel beam cooling mechanism for muons, and it would be significantly smaller and cheaper than other cooling channel designs. Realistic designs are still being explored, but the first simulations of particle tracking in the inverse cyclotron, with accumulation in the cyclotron core, have been done with electrostatic simulations in the particle-in-cell code VORPAL. We present an overview of the muon inverse cyclotron concept and recent simulation results.

Abstract:
Muon colliders and neutrino factories are attractive options for future facilities aimed at achieving the highest lepton-antilepton collision energies and precision measurements of Higgs boson and neutrino mixing matrix parameters. The facility performance and cost depend on how well a beam of muons can be cooled. Recent progress in muon cooling design studies and prototype tests nourishes the hope that such facilities could be built starting in the coming decade. The status of the key technologies and their various demonstration experiments is summarized. Prospects "post-P5" are also discussed.